This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Hey vokinyi623@gmail.com — ready when you are. Here are the calculations for the solid: Given: Diameter D = 10 cm Radius r = (D)/(2) = (10)/(2) = 5 cm Height of cylindrical part h_cyl = 15 cm Slant height of conical part l = 13 cm = 3.142 a) Height of the solid Step 1: Calculate the height of the conical part (h_cone). Using the Pythagorean theorem for the cone: l^2 = r^2 + h_cone^2. 13^2 = 5^2 + h_cone^2 169 = 25 + h_cone^2 h_cone^2 = 169 - 25 h_cone^2 = 144 h_cone = sqrt(144) = 12 cm Step 2: Determine the height of the hemispherical part (h_hemi). The height of the hemispherical part is equal to its radius. h_hemi = r = 5 cm Step 3: Calculate the total height of the solid. The total height is the sum of the heights of the conical, cylindrical, and hemispherical parts. H_total = h_cone + h_cyl + h_hemi H_total = 12 cm + 15 cm + 5 cm H_total = 32 cm The height of the solid is 32.0 cm. b) Volume of the solid, correct to 1 decimal place Step 1: Calculate the volume of the conical part (V_cone). V_cone = (1)/(3) r^2 h_cone V_cone = (1)/(3) × 3.142 × (5 cm)^2 × 12 cm V_cone = (1)/(3) × 3.142 × 25 × 12 cm^3 V_cone = 3.142 × 25 × 4 cm^3 V_cone = 314.2 cm^3 Step 2: Calculate the volume of the cylindrical part (V_cyl). V_cyl = r^2 h_cyl V_cyl = 3.142 × (5 cm)^2 × 15 cm V_cyl = 3.142 × 25 × 15 cm^3 V_cyl = 1178.25 cm^3 Step 3: Calculate the volume of the hemispherical part (V_hemi). V_hemi = (2)/(3) r^3 V_hemi = (2)/(3) × 3.142 × (5 cm)^3 V_hemi = (2)/(3) × 3.142 × 125 cm^3 V_hemi = (785.5)/(3) cm^3 V_hemi ≈ 261.8333 cm^3 Step 4: Calculate the total volume of the solid. V_total = V_cone + V_cyl + V_hemi V_total = 314.2 cm^3 + 1178.25 cm^3 + 261.8333 cm^3 V_total = 1754.2833 cm^3 Rounding to 1 decimal place: V_total = 1754.3 cm^3 The volume of the solid is 1754.3 cm^3. c) Surface area of the solid, correct to 1 decimal place Step 1: Calculate the curved surface area of the conical part (CSA_cone). CSA_cone = r l CSA_cone = 3.142 × 5 cm × 13 cm CSA_cone = 3.142 × 65 cm^2 CSA_cone = 204.23 cm^2 Step 2: Calculate the curved surface area of the cylindrical part (CSA_cyl). CSA_cyl = 2 r h_cyl CSA_cyl = 2 \